Approximating functions with Taylor polynomials and error bounds

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Intros
Lessons
  1. Approximating Functions with Taylor Polynomials and Error Bounds

    i) Taylor Polynomials and the Error Term

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Examples
Lessons
  1. Approximate ln 2 using the 3'rd degree Taylor Polynomial. Find the error term.
    1. Find the 4th degree Taylor Polynomial centred around a=0a=0 of f(x)=exf(x)=e^x. Then approximate e2e^2.
      1. Find the 2nd degree Taylor Polynomial centred around a=1a=1 of f(x)=(x+1)f(x)=\sqrt{(x+1)} and the error term where x[0,2]x \in [0,2].
        1. Show that f(x)=exf(x)=e^x can be represented as a Taylor series at a=0a=0.
          1. Show that f(x)=cos?xf(x)= \cos ?x can be represented as a Taylor series at a=0a=0.